The Gunners inflicted a first Premier League defeat on Solskjaer since he took over from Jose Mourinho at Old Trafford as they ran out 2-0 winners at the Emirates Stadium on Sunday.
Solskjaer, who had previously also not lost an away game since becoming interim boss at Old Trafford, was criticised for his tactics in north London while some claimed his players seemed tired following their dramatic Champions League win over Paris Saint-Germain five days earlier.
But Solskjaer has hit back at claims that his side put in an underwhelming display, telling a press conference: "You’re always measured on results but we played a good game against Arsenal.
"We have played so much worse and won games and that’s the strange thing when you’re a manager. You can look behind the result and say that was a good performance that didn’t get what it deserved.
"It’s so strange, the Arsenal one, very disappointed in the result and it hurts more than anything. But we can’t look at the performance and say we were sh*t because we weren’t, to be honest and blunt. We weren’t. We played well."
Man Utd have reached the final of the competition twice in the last three years, beating Crystal Palace at Wembley Stadium in Louis van Gaal's final game in charge in 2016 before Mourinho's side lost to Chelsea in 2018.
It remains one of two trophies the current squad remain in contention for following their progress to the quarter-finals of the Champions League, and Solskjaer is now focused on ending the season positively and pushing for silverware.
"We’ve done well. We’ve given ourselves the chance to be in and amongst the top four, we’re in the quarter-finals of both the FA Cup and Champions League.
"We’ve been on a good run, but it's not squeaky bum time like the gaffer [Sir Alex Ferguson] used to say but it tightens up in April and May at Manchester United.
"We narrow the focus and it’s now about winning trophies and making use of the squad."
Man Utd's results under Solskjaer have led to overwhelming support for him to be given the manager's job on a permanent basis.
Former team-mate Gary Neville has insisted that the Norwegian should be offered a long-term contract during the upcoming international break, but Solskjaer insists he is not looking any further than the end of the season.
"I didn’t have a schedule, I had until May to do whatever I could with the team, playing style and mood, and everything has been going well.
"But then again football kicks you in the teeth sometimes and there’s always the next day. If we get through to the semi-finals of the FA Cup then I’ll have a nice few days back home."